Goal-oriented communication has become one of the focal concepts in sixth-generation communication systems owing to its potential to provide intelligent, immersive, and real-time mobile services. The emerging paradigms of goal-oriented communication constitute closed loops integrating communication, computation, and sensing. However, challenges arise for closed-loop timing analysis due to multiple random factors that affect the communication/computation latency, as well as the heterogeneity of feedback mechanisms across multi-modal sensing data. To tackle these problems, we aim to provide a unified timing analysis framework for closed-loop goal-oriented communication (CGC) systems over fading channels. The proposed framework is unified as it considers computation, compression, and communication latency in the loop with different configurations. To capture the heterogeneity across multi-modal feedback, we categorize the sensory data into the periodic-feedback and event-triggered, respectively. We formulate timing constraints based on average and tail performance, covering timeliness, jitter, and reliability of CGC systems. A method based on saddlepoint approximation is proposed to obtain the distribution of closed-loop latency. The results show that the modified saddlepoint approximation is capable of accurately characterizing the latency distribution of the loop with analytically tractable expressions. This sets the basis for low-complexity co-design of communication and computation.

翻译：目标导向通信因其提供智能、沉浸式与实时移动服务的潜力，已成为第六代通信系统的核心概念之一。新兴的目标导向通信范式构成了融合通信、计算与感知的闭环系统。然而，由于影响通信/计算时延的多种随机因素，以及跨模态感知数据反馈机制的异构性，闭环时序分析面临挑战。为解决这些问题，我们旨在为衰落信道下的闭环目标导向通信系统建立一个统一的时序分析框架。该框架具有统一性，因其考虑了不同配置下闭环内的计算、压缩与通信时延。为刻画跨模态反馈的异构性，我们将感知数据分别归类为周期反馈型与事件触发型。我们基于平均性能与尾部性能构建时序约束，涵盖CGC系统的时效性、抖动性与可靠性。提出了一种基于鞍点近似的方法以获取闭环时延的分布。结果表明，修正的鞍点近似能够以解析可处理的表达式准确刻画闭环时延分布，从而为通信与计算的低复杂度协同设计奠定基础。